Opening a Sphere Mesh
Create a sphere, move the pivot point to the point where you want the mouth to open.



Duplicate. On one sphere delete the top half. On the other delete the lower half.


Animate both objects by rotating them in opposite directions.



Optionally create a cycle by extrapolating the keyframes in the curve editor (Channel->Extrapolate->Make cyclic).

Add an empty and parent both hemispheres to it.

To move the object just move the empty.